The present invention relates to an optical signal processing system and method; and more particularly, it relates to an optical signal processor wherein two separate optical images are combined in such a manner that the output optical image is a predetermined mathematical function of the information contained in the separated input images.
The inherent two-dimensional parallel processing capabilities of coherent optical systems have led to many diverse applications of optical processing. A vast majority of these applications have been concerned with spatial frequency processing of two-dimensional data such as photographs. The development, by Vander Lugt, of a holographic technique to produce complex spatial filters has enabled the mathematical operations of convolution and correlation to be applied in the analysis of two-dimensional data. The implementation of these filters has further diversified the applications of optical processing. However, the application of these optical techniques to the analysis of one-dimensional data has been quite limited even though many of the advantageous properties of optical computation are also applicable to the processing of such data. The present invention, thus, is directed to an optical system which will enable instantaneous and simultaneous spectral analysis of two signal records or images; and, with the use of a simple narrow slit spatial filter in the frequency plane, the operations of convolution and correlation of the two signal images can be obtained without the need to holographically record the frequency spectrum of one signal record prior to processing.
The present invention has utility in the comparison of one optical image with a second optical image, and it could be used, for example, as a medical diagnostic system. In this case, again as an example, one of the input images would bear information representative of a reference electrocardiogram (ECG) or an earlier ECG of the same patient. The second optical image could be a more recent ECG of the patient. Simply by placing the two optical images in the present system, there is immediately produced a correlation or convolution of the two input images; and the output is immediately present in optical form so that it is easily read electronically or stored on film, for example.
For an electronic system to be capable of performing similar computational functions, such as correlations or convolutions, of two independent input signals as complex as ECGs, the system would have to require a substantial amount of costly hardware such as analog-to-digital converters, and also possess substantial computational capacity. Even then, it would take some time for the output results to be generated.
In the present invention, the input information is stored on optical transparencies in a "density-modulated" form. As used herein, a "density-modulated transparency" is one in which the density of the image bearing the information is modulated such that the light amplitude transmission of the transparency is proportional to the amplitude of the signal to be processed. The intensity of light is proportional to the square of the amplitude, and whereas physical systems deal with light intensity rather than light amplitude, this distinction should be borne in mind throughout. The transparencies bearing the input information are density-modulated only in one direction, called the "information" axis. For example, the density of the image may vary left-to-right, but will remain constant along all vertical lines. Methods of recording information on transparent film by density modulation are known in the art, and some of these methods are discussed below. In summary, the information to be processed is recorded on an optical transparency as a spatial light amplitude variation along the information axis.
The mathematical and physical principles of optical computing are based primarily on the phenomenon of diffracted monochromatic light and the inherent optical properties of a thin converging lens. The information to be processed by this technique is recorded on an optical transparency as a spatial light amplitude variation. Illuminating this transparency with monochromatic light results in diffraction of the light in a manner determined by the amplitude and phase at each point on the back side of the transparency. The function of the thin converging lens is to focus the diffraction pattern on an appropriate plane behind the lens. The resultant amplitude and phase of the light distribution across this plane is directly proportional to the two-dimensional Fourier transform of the light amplitude transmitted by the input transparency--thus this plane is sometimes referred to as the frequency plane.
An optically produced one-dimensional Fourier transform is a special case of this two-dimensional transformation. Optical processing of one-dimensional data, such as biological signals, requires an initial conversion of the signal into the spatial domain. This may be accomplished by properly recording the signal on an optical transparency such that the light amplitude transmittance as a function of one spatial coordinate is directly related to the input signal amplitude as a function of time. Illuminating this transparency with coherent light will produce an optical Fourier transform pattern behind the converging lens. The light amplitude distribution along one spatial coordinate in the transform plane will be directly related to the one-dimensional Fourier transform of the input signal.
According to the present invention, then, a point source of monochromatic light is focused by a thin converging lens onto the frequency plane. Between the source and the frequency plane, two one-dimensional density-modulated transparencies are placed together in the light path. The tranparencies extend perpendicular to the light path. One transparency may contain reference data. The other transparency may contain the "input" information desired to be processed or compared. The two transparencies are oriented relative to each other such that their information axes define a predetermined angle. In other words, the density-modulated information on each transparency is one-dimensional in the sense that the information is contained only along the information axis. When the two transparencies are juxtaposed, the information axes are placed at a 90.degree. angle.
By placing the two transparencies as just described, the product of the Fourier transforms of the two independent input signals will appear along a line in the frequency plane. This line, if taken along the +45.degree. axis will contain information representative of the product of the two transforms; and if taken along the -45.degree. axis, it will also be the product of the two transforms. However, the argument of frequency in one of the functions will be minus in the latter case.
Thus, a slit is arranged in the frequency plane, for this example, at an angle of plus or minus 45.degree. depending upon whether a convolution or correlation function is desired. The only information that passes through the slit, therefore, is the product of the two transforms at an angle of the slit. Thereafter, an inverse transform is performed by a thin converging lens onto an image plane. In optics, a second transformation is the same as an inverse transformation, as explained above.
Thus, the second converging lens produces an image of the input transparencies at the output or image plane, performing a Fourier transform from the frequency plane to the image plane, which transform is an inverse Fourier transform mathematically.
Output information is obtained by scanning the image plane in a direction parallel to the direction of elongation of a slit in the frequency plane. The result is a measurement of light intensity which is the square of the convolution or correlation function (again, because a physical system deals with intensity, not light amplitude).
An alternative embodiment is also disclosed wherein only a single converging lens is used to obtain the same results. It will be appreciated by persons skilled in the art that the light source need only be a point source of monochromatic light of fairly large intensity--it need not necessarily be coherent light.